Recent developments in spectral synthesis for exponential systems and\n for non-self-adjoint operators

2012/12/25 by Anton Baranov, Baranov, Anton, Yurii Belov +5 · 2 citations
Mathematics · #Spectral Theory in Mathematical Physics #Differential Equations and Boundary Problems #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1212.6014

Abstract

We survey recent results concerning the hereditary completeness of some\nspecial systems of functions and the spectral synthesis problem for a related\nclass of linear operators. We present a solution of the spectral synthesis\nproblem for systems of exponentials in L²(-\π, \π). Analogous results are\nobtained for the systems of reproducing kernels in the de Branges spaces of\nentire functions. We also apply these results (via a functional model) to the\nspectral theory of rank one perturbations of compact self-adjoint operators.\n

Cited by

• Spectral synthesis in de Branges spaces
• One-dimensional perturbations of unbounded selfadjoint operators with empty spectrum

Related

• Hereditary completeness for systems of exponentials and reproducing kernels
• Completeness and spectral synthesis of nonselfadjoint one-dimensional\n perturbations of selfadjoint operators
• Hereditary completeness of Exponential systems \e^{λ_n t}\_n=1^∞ in their closed span in L² (a, b) and Spectral Synthesis
• Spectral synthesis for exponentials and logarithmic length
• Spectral theory of rank one perturbations of normal compact operators